A spokesman for Sir Cliff said on Saturday night: "Today Sir Cliff Richard voluntarily met with and was interviewed by members of South Yorkshire Police. He was not arrested or charged.

"He co-operated fully with officers and answered the questions put to him. Other than restating that this allegation is completely false and that he will continue to co-operate fully with the police, it would not be appropriate for Sir Cliff to say anything further at this time."

Sir Cliff was in Portugal when the search of his flat took place on August 14.

His fans have rallied round the veteran star since the allegation became public and are showing their support by buying copies of his 1992 Number Seven hit I Still Believe In You with the song headed for this weekend's Top 40.

It emerged earlier this week that he has pulled out of a visit to the US Open tennis championships and turned down the freedom of his adopted Portuguese home city of Albufeira.

He also cancelled an appearance at a charity event at Canterbury Cathedral next month because he did not want the event to be "overshadowed by the false allegation".

Meanwhile the BBC has been accused of a "cover-up" over its role in the raid by officers from South Yorkshire and Thames Valley police.

South Yorkshire police chief constable David Crompton claimed the corporation appeared to "distance itself from what had happened" after it broadcast the raid on the pop star's penthouse.

The BBC, which had a film crew on the scene, broke the news of the search but has been heavily criticised for its handling of the story.

Mr Crompton said the BBC's misleading and inaccurate portrayal of its involvement in what happened led to the force making a formal complaint.

Keith Vaz, home affairs committee chairman, said the claims were a "matter of deep concern".

He has summoned the chief constable and BBC director general Tony Hall to appear before the committee on September 2.

Mr Crompton said the force was approached by a BBC journalist with detailed information about its investigation.

It "reluctantly agreed" to give the reporter notice of the day officers planned to search the property to dissuade the corporation from publishing details in advance and protect the "integrity of the investigation".

"It was not done in order to maximise publicity, contrary to some press reports," he wrote in a letter to Mr Vaz.

Mr Crompton said an article appeared on the BBC website on the afternoon of the raid that suggested there had been a deliberate attempt to "ensure maximum coverage" by the force.

"The force contacted the BBC but the corporation refused to withdraw or adapt the article," he said in the letter.

"This appeared to be an attempt by the BBC to distance itself from what had taken place and cover up the fact that it had initiated contact with the force about the story.

"This was misleading and was known by the BBC to be inaccurate."

Lord Hall has insisted that BBC journalists "acted appropriately" in its coverage of the story.

A BBC spokesman said: "We have set out our position. The story was clearly in the public interest. The police complained specifically about an analysis piece on the BBC website and subsequently, and highly unusually, we confirmed that South Yorkshire Police was not the source of our story."